How do I identify the number and type of objects in the same picture?
Your problem might involve a combination of object recognition (or object classification), which is the problem of determining which objects are in an image, and object detection (which could also be called object localization), which is the task of locating a specific object in the image. 

A naive approach to solve your problem would then be to first locate the position of all possible objects in the image (object detection), then, for each these positions, perform object recognition (or classification). Then you would count the number of detected and classified objects for each possible class.

There are several models that can be used to solve your problem. 

The YOLO (You Only Look Once) model (introduced in the paper You Only Look Once: Unified, Real-Time Object Detection) (2016) can be used to detect multiple objects in an image. See the official YOLO implementation, which is part of the Darknet framework. Have also a look at this article, which explains how to use the official implementation of YOLO. 

You could also use the SSD model (introduced in the paper Single Shot MultiBox Detector). There is also R-CNN (Regions with CNN features), Fast R-CNN or Faster R-CNN, but these should perform worse than both YOLO and SSD.

So, even if you do not care about the locations, YOLO (and other mentioned methods) can give them to you, in addition to the number and type of objects in the image.